The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. 38, Part II
ASSESSMENT OF EXTENSIONAL UNCERTAINTY MODELED BY RANDOM SETS ON
SEGMENTED OBJECTS FROM REMOTE SENSING IMAGES
X. Zhao a, b, X. Chen a, c, *, L. Tian a, T. Wang b, A. Stein b
a
State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University,
Luo Yu road 129, China – (cxl, tianliqiao)@lmars.whu.edu.cn
b
International Institute for Geo-Information Science and Earth Observation, Hengelosestraat 99, Enschede,
Netherlands – (xzhao, tiejun, stein)@itc.nl
c The Key Lab of Poyang Lake Ecological Environment and Resource Development, Jiangxi Normal University,
Nanchang, Jiangxi, China
Commission II, WG II/4
KEY WORDS: accuracy assessment, uncertainty, random set, image segmentation, Poyang Lake
ABSTRACT:
A newly developed random set model has been applied to model the extensional uncertainty of a wetland patch. The objective of
this research is to explore the corresponding variables collected on the ground for validating the uncertain image objects and to
report the quality of the random set modeling. The independent samples t-test and a correlation analysis have been used to identify
the main variables, whereas the overall accuracy and Kappa coefficients quantify the quality of the random set model. The results
show that significant correlations exist among covering function, Carex coverage and NDVI. This suggests that the covering
function of the random set can be quantified and interpreted adequately by NDVI derived from satellite images and Carex coverage
measured in the field. In addition, the core set of the random set has an overall accuracy of 85 percent and a Kappa value equal 0.54,
being higher than the median set and support set. We conclude that the random sets modeling of uncertainty allows us to perform an
adequate accuracy analysis.
1. INTRODUCTION
Conventional pixel-based and object-based classification
approaches generate maps with exclusive categories. These
hard classifications are designed for mapping discrete objects
and clear bounded land cover, but they are not appropriate for
mapping continuous landscapes in nature such as wetlands
(Woodcock and Gopal 2000). The limitation of hard
classification to represent transition zones and uncertain
boundaries has been a motivating factor for the development of
alternative approaches based on uncertainty handling theories
such as fuzzy set theory (Zadeh 1965) and random set theory
(Matheron 1975; Cressie 1993). A number of soft classification
and uncertainty modeling methods have been developed for
classifying and representing nature landscapes such as beach
(Van de Vlag and Stein 2007) and grassland (Zhao et al. 2009a),
and for modeling dynamic phenomena such as fire spread
(Vorob'ov 1996) and flooding (Stein et al. 2009a).
The accuracy assessment of soft classification results, however,
remains a theoretical and practical difficulty. Foody (2002)
gave overviews on accuracy assessment issues and current
challenges. For the pixel-based soft classification, such as fuzzy
classification, some research managed to perform validation by
fuzzy confusion matrix which was extended from conventional
assessment approach (Woodcock and Gopal 2000). Accuracy
assessment of extracted image objects by object-based
classification or segmentation has bigger challenge (Zhan et al.
2005), especially when objects are uncertain (Stein et al. 2009b).
The main difficulty is that the information about uncertainty
represented in the results does not always have corresponding
* Corresponding author.
202
objects in the field. This is because even on the ground, due to
vague and unambiguous boundaries, the delineation of
uncertain objects like a city may be impossible. In addition,
detailed reference data which is critical for validating soft
classification and uncertainty modeling results, are often
unavailable, especially when the historical field data was only
collected for hard classification.
Extensional uncertainty refers to the uncertainty in identifying
the geometric elements that describe the spatial extent of the
object (Molenaar 1998). Zhao et al. (2009b) have applied the
random set model to represent extensional uncertainty of
extracted image object from Landsat TM image in 2004. The
accuracy of the random set model derived from a historical
image is difficult to assess. Since the synchronous data with
detailed information are of a significant importance for
assessing model uncertainty, a clean and almost synchronous
HJ-1A image with comparable spatial resolution (i.e., 30 m)
two days before the survey was acquired. Moreover, the
sampling plan was specially designed for investigating zonation
pattern of wetland grassland and for accuracy assessment of
random set model before ground survey. The objective of this
research is twofold: (1) to explore the corresponding
measurable variables collected on the ground for validating the
uncertain image objects modeled by random sets, (2) to
quantify the quality of the random set modeling results.
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. 38, Part II
square, with the accuracy less than 10 m. Within the plots, the
following variables were recorded: land cover types, vegetation
types (communities or species), vegetation height, percent
vegetation cover and bird signs such as drops and falling feather.
Furthermore, five or eight subplots (1m * 1m) were also
established within some 30m * 30m plots to measure the less
homogeneous plots and took averaged variables. The spectral
characteristics of typical vegetation types were measured within
1m * 1m subplots using SVC field-portable spectroradiometer.
For each reading of the spectroradiometer, around 30 separate
measurements were taken, which were then averaged for each
1m * 1m subplot.
2. METHODS
2.1 Study Area and Image Pre-processing
The study area PLNNR (29°05′- 29°18′N, 115°53′-116°10
′E) is located to the northwest of the Poyang Lake in the
JiangXi province, central China. Nine lakes in the PLNNR are
connected to the Poyang Lake during the high water levels in
summer and disconnected when water levels are low in spring,
autumn and winter. All kinds of wetland vegetation are
blooming in spring and serve as important habitats and forages
for spring migrating birds. In the summer flooding time, grasses
growing at high elevations (e.g., Miscanthus) remain stand
above the water, whereas sedges (e.g., Carex) and submerged
aquatic species (e.g., Potamogeton) at lower elevations are
flooded beneath. When the flood is gone and winter migration
birds arrive in autumn from late September, only few kinds of
vegetation like Carex start to turn green again and thrive until
winter come. Other vegetation communities become senescent
in autumn and dead in winter. When sedges at the lower
elevations are shooting up gradually, different kinds of birds
forage on leaves and rhizomes of young sedges and rhizomes of
submerged aquatic species in different elevation zones. Taller
sedges also provide bird’s habitat and shelter (Wu and Ji 2002).
Wetland grassland has biggest width of zonation and also
largest area in Banghu, therefore, our ground survey was
carried out surrounding Banghu lake.
HJ-1A/B satellites were launched on Sept 6, 2008 from China.
One scene of a HJ-1A image on November 24, 2009 with 30m
resolution was applied and downloaded from the China Centre
for Resource Satellite Data and Applications (CRESDA). As a
second level product, radiometric correction and systematic
geometric correction have been done before downloading and
the image is under UTM WGS84 projection. A topographic
map of scale 1:10,000 in PLNNR was used as the geographic
reference data for more accurate geometric correction. The root
mean squared error of the geometric correction was less than 10
m. The Normalized Difference Vegetation Index (NDVI) was
calculated for the HJ image:
NDVI= ρ nir − ρ red
ρ nir + ρ red
where
ρ red
and
ρ nir
Fig. 1. Nine lakes in Poyang Lake National Nature Reserve
(dish line on the left figure) and sample plots along four
transects (L1-L4) on false colour HJ image (blue dots on the
right figure).
2.3 Image
modelling
segmentation
and
extensional
uncertainty
Random set theory has been employed as a foundation for the
study of randomly varying populations and randomly varying
geometrical shapes (Stoyan and Stoyan 1994) and thus applied
in our previous research for modelling extensional uncertainty
of image objects (Zhao et al. 2009a). In this research, our target
object is the Carex patch which is located on the east bank of
Banghu (Fig. 1). Since Carex is the dominant green vegetation
in October, we use NDVI image as input for the region growing
segmentation. Based on a threshold range (minimum and
maximum pixel values), the region growing algorithm expands
from a small seed combining connected pixels within prespecified limits (Russ 2007). Vegetation patches with vague
boundaries are sensitive to the setting of parameters in the
region growing algorithm. Therefore, by slightly changing the
parameters, e.g., under normal distribution with a small value of
variance, and segmenting iteratively, a set of resulting objects
established a random set (Zhao et al. 2009a; b). The image
object with extensional uncertainty thus was modeled by the
generated random set.
(1)
stand for the spectral reflectance
measurements acquired in the red and near-infrared band,
respectively.
2.2 Ground Survey
From October 26th until November 6th, 2009, a ground survey
was carried out around Banghu lake to investigate the zonation
pattern of wetland grassland. Although it is assumed that for a
random set modeling, some versions of random sampling
preferably stratified unaligned random sampling be used rather
than a systematic sampling. But in order to verify the gradual
change of vegetation and restricted by accessibility and costs,
four typical transects have been designed, starting from the
river bank and perpendicularly crossing different zonations
until they reach the lake bank of Banghu (Fig. 1). These four
transects have 27, 24, 14, 8 sample plots respectively, so that 73
plots have been sampled in total.
The procedure is as follows: Firstly, the growing seed was
selected inside the central interior part of the target object. Then
we initialized the parameters, i.e., upper and lower threshold.
For each parameter, a random number was generated from a
normal distribution with the initialized parameter as the mean
and a preset variance. Fourthly, start the segmentation and
obtain object Oi as one sample of the random set. Iterating the
above steps several times and a set of resulting objects establish
Sample plots with size of 30m * 30m are distributed evenly
along transects, and were fixed by measuring tape. The location
of each sample plot was measured by GPS at the centre of the
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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. 38, Part II
height appears at high elevations near the river bank, often
mixed with Cynodon, Carex, Polygonum, and human planted
poplar. Some of the flowered Miscanthus also has green leaves
of lower height, or some shorter Miscanthus is not flowered, we
call them green Miscanthus in this paper. If large number of
cattle graze on Carex, as for example in L2, the Miscanthus is
cut to approximately 0.5 m. The second zone is Carex dominant
zones, which across approximately 500 m horizontal distance.
The height of Carex ranges from 0.3 to 0.6 m, and they thrive,
with very high density. As forward to the lake bank, the height
and density of Carex are decreasing and Polygonum, Artemisia
and Eleocharis appear and mixed with it. The third zone is near
the lake bank where elevation changes gradually. The indicators
of low elevation are high soil moisture and plant like
Cardamine and young Carex. The farthest place we reached on
the lake bank in L1 is covered by 10 cm shallow water and dead
Potamogeton and Vallisneria beneath. We found birds’ drops
and feathers frequently and the birdcall is very clear. On the
bank of L2-4, we found wet soil, Cardamine, dead and dry
Potamogeton and Vallisneria covered on soil, and shooting up
Carex with very low density.
a random set. Several characteristics of random set can be used
to describe the extensional uncertainty of objects. For example,
n polygons resulting from n times segmentation are samples of
the random set, denoted as O1, . . ., On. The probability that
pixel x ∈ R2 occupied by the random region can be determined
by
PrU n Oi ( x) .
i=1
An estimator of the covering function of
random set Γ is obtained as:
1 n
PrΓ ( x) = ∑ I Oi ( x ), x ∈ R 2
n i=1
Where
I Oi (x)
(2)
is the indicator function of Oi(x). The covering
function can be interpreted as the probability of the pixel x on
space R2 being covered by the random set. All the pixels with
covering function equal to or larger than p construct a p-level
set of the random set. The 0-level set, 0.5-level set and 1-level
set are called support set, median set and core set respectively.
In practice, we can adjust the support set to 0.05-level set and
core set to 0.95-level set, in order to avoid extreme outliers.
Further theoretical details about random set models and
technical details about segmentation can be found in our
previous work (Zhao et al. 2009a; b).
After analyzing the field data, we found that pixels with pure
Carex have maximum NDVI values around 0.6, whereas 50
percent Carex coverage corresponds to NDVI values around
0.45. Since plots with NDVI larger than 0.6 are dominated by
Carex, to simplify the random set generation procedure, we
fixed 0.7 as the maximum threshold in region growing
segmentation and do not apply randomization on it. On the
other hand, we selected 0.45 as the initialized minimum
threshold, and generated 100 random numbers from normal
distribution with mean equal to 0.45 and σ2 equal to 0.1. Finally,
we placed the growing seed at the location of one sample plot
where 100 percent Carex was recorded, and used the 100
randomized threshold intervals to obtain 100 objects and
modelled them as a random set Γ.
2.4 Accuracy assessment
Figure 2 shows dominant vegetation types and their coverage at
27 sample plots along transect L1. As illustrated in the legend,
the length of the bar indicates the percent coverage of
vegetation which is averaged from 5 or 8 subplots. The average
height of each vegetation type can be read from the centre point
of the bar according to the scale on the left. For the three
zonations we categorized above, samples from 1 to 5 belong to
the first zone, and samples from 20 to 27 belong to the third
zone. Samples from 6 to 12 are relatively homogenous and
belong to the second zone, whereas samples from 13 to 17 are
in transition area. From the NDVI values extracted from HJ
image at corresponding sample plots, we found the NDVI
achieve the peak around 0.6 at sample 8 until sample 12, where
either homogenous Carex plots appear or Carex mixed with
green Miscanthus. As the Carex goes shorter forward the lake,
the coverage of wet soil and dead Potamogeton increase and
NDVI values reduce to 0.2 and remain stable.
3.2 Corresponding variable in the field
In order to validate the modelling result, all the 73 sample plots
are used for accuracy assessment. The overall accuracy (OA),
producer accuracy (PA), user accuracy (UA) and kappa
coefficient are derived from error matrix. Each of these
provides a different summary of the information contained in
the error matrix. A widely applied kappa z-test (Congalton et al.
1983) is also used to test for statistically significant differences
in accuracy of outputs. Independent samples t-tests in SPSS
software were adopted to determine if the mean value of the
Carex coverage is different for sample plots which are included
and excluded by the median set. Moreover, correlation between
Carex coverage, NDVI and covering function value were
quantified by regression models.
In the ground survey, we measured as many variables as we can
in 1m * 1m subplots, including land cover type, vegetation
species, percent coverage, height and spectral curve, to detail
the field information for accuracy assessment. We compares
field measured NDVI values of vegetation, to which different
vegetation types, coverage and heights contribute differently.
First of all, plots covered by lower percent vegetation coverage
will have lower NDVI. The cases of Carex with coverage 100,
70, 30, 5 percents show obviously decreasing NDVI. Secondly,
vegetation with different heights may have the same NDVI. For
example, pure Carex plots with height between 0.4 and 0.6
meter are have the same NDVI value 0.89. The possible reason
is Carex extremely thrive at that heights and with very high
growing density, which cause NDVI be fully saturated. Thirdly,
for cases where NDVI does not achieve saturation, e.g. four
Miscanthus plots with 100 percent coverage, the height of the
plant shows its impact on NDVI. We measured both the height
of flowered part and green leaves part of Miscanthus. The
flowered parts of Miscanthus are dry in autumn, thus having
low
NDVI
around
3. RESULTS
3.1 Ground survey
From the river bank to the lake bank, transects L2-4 are
approximately 2000 m long, whereas L1 is approximately 1200
m. Three different zones occur along all the four transects. The
first zone is on the river bank. Flowered Miscanthus of 1-2 m
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Height
>1
NDVI
NDVI
1
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0
1 2 3
River Bank
4
5
6
100
Percent
coverage
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Lake bank
100
50
100
50
30
10
Carex
30
10
5
100
50
Green Miscanthus
30
10
5
100
50
Cardamine
Cynodon
5
50
30
10
5
Miscanthus flower
Dead Miscanthus
30
10
5
Dead Potamogeton
Wet soil
Fig. 2. Types of dominant vegetation, their percent coverage and heights along transect L1 are compared with NDVI extracted from
corresponding pixels at field samples
We found that these three curves have similar trends along
the transect L1. They have peak values approximately from
sample 6 to 12 and low values at the two ends. Both curves
of CF and NDVI have relatively gentle slope from sample 1
to 7, compared with steep slope from sample 15 to 27. But
PCC decreases rapidly from sample 6 to sample 1, making a
steep slope at the left end of the curve. This mismatch can be
explained by the mixture of green Miscanthus with Carex
(Fig. 2), which also contribute to the NDVI. At the right end
of the curves, although PCC has values around 20 percent,
but due to the low height and low density of young Carex
(Fig. 2) contributing little to NDVI value, the CF shows 0
values from sample 18 to sample 27.
0.25. Since the NDVI is not saturated when flowered part
exist, the NDVI values reduce as heights of their green leave
part decreasing. Last but not least, vegetation growing
density also influences the NDVI value. For example,
Artemisia is kind of plant which also thrive in autumn, but
with very low proportion and usually mixed with Carex. For
plots which are fully covered by Carex and Artemisia at the
same height of 0.4 meter, Artemisia has lower NDVI of 0.79
compared with 0.89 for Carex. The possible reason is that
coverage percent only reflects the proportion of the projected
canopy of vegetation on the ground, so that Carex with high
density has larger NDVI than Artemisia.
According to the results above, we found that Carex
coverage is an outstanding variable which is closely related
to NDVI, may act as the corresponding variable of covering
function derived from the random set model. For the other
variables, they are closely related with each other when
contributing to NDVI value and can not be act as
independent variable.
3.3 Extensional uncertainty modelled by random sets
Main Characteristics of random set Γ, including the covering
function, the support set, the median set, the core set and the
variance, were estimated. The contours of support, median
illustrated in Fig. 3a indicate the possible spatial extension of
this Carex patch with above 0.05 probabilities and above 0.5
probabilities respectively. The pixels with covering function
value larger than 0.95 are enclosed by the contour of core set
which almost ensure the pixel belonging to Carex patch. The
differences between the spatial extension of support set and
core set indicate the extensional uncertainty of Carex patch.
The higher uncertainty corresponds to higher variance of
random set in Fig. 3b.
Fig. 3. Extracted object and its extensional uncertainty
described by concepts from random set theory: (a) support
set, median and core set (b) variance
T-test was then used to explore the relationship between
median set and Carex coverage. The null hypothesis is that
the mean value of the Carex coverage of samples which
included by the median set is equal to the mean value of the
Carex coverage of samples which excluded by the median set.
The two-tailed p value associated with the test p = 0.000
which is smaller than 0.05, then we reject the null hypothesis.
That implies that there is sufficient evidence to conclude that
samples included and excluded by the median set have
different Carex coverage.
3.4 Linking covering function to Carex coverage
By plotting the field data and estimated covering function,
the values of the covering function (CF) were compared with
NDVI and percent coverage of Carex (PCC) for all the
sample plots, among which in transect L1 are shown in Fig. 4.
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indicate that these two classes are reliable in support set and
core set respectively. Presence of Carex has high UA and
low PA in core set, showing that there is more area of Carex
in the field than is indicated by the core set. Absence of
Carex has both low PA and UA in support set, because 12
out of 16 samples which are classified as absence correspond
to presence in the field data. The possible explanation for the
unsatisfied accuracy is that the grouping criteria of making
testing samples for the support set is not appropriate. We get
supporting evidences from sample 18 to sample 24 in Fig. 4.
These samples have 0 covering function, and not belong to
the support set, but they still have 20 percent Carex at low
height and with low density. This result suggests that the
support set is not sensitive to the Carex coverage lower than
20 percent.
Fig. 4. Percent coverage of Carex, NDVI and covering
function at sample plots compared along transect L1
A kappa z-test for pair-wise comparison in accuracy shows
that there was significant difference between the support set
and other sets, but no significant difference between the core
set and the median set. The results suggest the quality of the
core set and the median set is significantly higher than that of
the support set.
Table 1 highlights that the correlations between covering
function and Carex coverage were observed with the R2values ranging from 0.46 to 0.71, whereas correlations
between covering function and NDVI have higher R2-values
ranging from 0.82 to 0.97. For the total 73 samples, although
Carex coverage has lower R2-value with covering function
than with NDVI, but it still explains 54% of variation in
covering function and the relationship is significant at 0.01
confidence level. This relationship suggests that covering
function of the random set can be quantified and interpreted
adequately by either NDVI from image or Carex coverage
from the field data. The relationship between Carex coverage
and NDVI with 0.56 R2-value suggests that NDVI is closely
related to Carex coverage at the time the image acquired.
This result also supports our previous decision that using
NDVI image as input to extract Carex patch.
Table 2. Comparison of OA, UA, PA and kappa coefficients
for the core set, the median and the support set. C1 indicates
class presence of Carex and C2 for class absence of Carex.
Core set
PA (%)
UA (%) OA (%)
Kappa
C1
47
90
85
0.54
C2
98
84
Median set
C1
76
85
77
0.52
C2
78
66
Support set
C1
82
93
78
0.22
C2
50
25
Table 1. R2-values of the correlation relationships between
covering function (CF) and percent coverage of Carex (PCC)
and NDVI for four transects separately and in total
Transect
L1
L2
L3
L4
L1-L4
CF-PCC
0.67
0.51
0.71
0.46
0.54
CF-NDVI
0.97
0.91
0.82
0.91
0.93
PCC-NDVI
0.63
0.62
0.63
0.48
0.56
4. CONCLUSION AND DISCUSSION
In this research, we applied the random set model for
representing uncertain boundary of a Carex patch, and
perform accuracy assessment on the modelling results. We
found that Carex coverage can be the corresponding variable
collected on the ground, by which the covering function of
random sets can be quantified and interpreted adequately.
The core set of the random set has higher accuracy than the
median set and the support set.
3.5 Accuracy assessment of the extracted uncertain
object
In order to validate the uncertain object, percent coverage of
Carex recorded for each sample plot were used to group
testing samples. The accuracy assessment was applied to the
support set by comparing with all the samples where Carex
appears, to the median set by samples where above 50
percent of area is dominated by Carex, and to the core set by
samples which are 95 percent covered by Carex. In each
error matrix, number of samples belongs to tow classes:
presence of Carex and absence of Carex are indentified.
Table 2 details the mapping accuracy of the support set, the
median set and the core set by OA, PA, UA and kappa
coefficient derived from error matrix. The highest overall
accuracy was achieved by the core set with OA of 85 percent
and kappa 0.54. According to (Mather 1999), the core set and
the median set have moderate kappa value, whereas the
support set has poor kappa value. By further looking at each
class, we find that presence and absence of Carex has high
PA and UA for support set and core set respectively, which
Significant correlations were found among covering function,
Carex coverage and NDVI, which suggests that covering
function of the random set can be quantified and interpreted
adequately by NDVI derived from image and Carex
coverage measured in the field. For the other variables, such
as vegetation types, height and density and coverage, they
also influence the modelling result, and should be considered
together. These variables, however, may belong to different
scales, such as nominal (e.g. vegetation type), ordinal (e.g.
big or small density) and ratio scale (e.g. height and
coverage). So they are difficult to integrate into one general
variable which might be better match with the covering
function of random set.
The quality of the random set models was assessed
quantitatively by OA, UA, PA and the kappa coefficients.
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Russ, J. C., 2007. The Image Processing Handbook. Taylor
& Francis.
The accuracy of core set is better than that of the median set
and much better than that of the support set. Since the
support set is not sensitive to the young Carex with coverage
less than 20 percent, inappropriate criteria for grouping test
samples might be the reason for its poor accuracy. This result
suggests that the random set model has a better performance
on the high coverage area and criteria for validating the
support set should be determined not only based on the
coverage. Moreover, it supports that Carex coverage cannot
be the only variable fully explaining the covering function
and other variables such as height should be considered
especially when the coverage is low.
Stein, A., P. Budde and M. Z. Yifru, 2009a. Stereology for
Multitemporal Images with an Application to Flooding.
Research Trends in Geographic Information Science. G.
Navratil (eds.). Springer-Verlag, pp. 135-150.
Stein, A., N. A. S. Hamm and Y. Qinghua, 2009b. Handling
uncertainties in image mining for remote sensing studies.
International Journal of Remote Sensing, 30, pp. 5365-5382.
Stoyan, D. and H. Stoyan, 1994. Fractals, Random Shapes
and Point Fields. John Wiley&Sons.
The accuracy of random set model applied in this study is
just moderate according to the assessment report. Several
reasons could contribute: on one hand, the parameters in the
region growing segmentation algorithm need further
adjustments. On the other hand, the field data which are often
referred as the ground truth may not perfectly match with
modeling results. In this study, more factors such as heights
and density of vegetation should be integrated with
vegetation coverage as united reference data for accuracy
assessment.
Van de Vlag, D. E. and A. Stein, 2007. Incorporating
uncertainty via hierarchical classification using fuzzy
decision trees. IEEE Transactions on geoscience and remote
sensing, 45(1), pp. 237-245.
Vorob'ov, 1996. Random set models of fire spread. Fire
technology, 32(2), pp. 137-173.
Woodcock, C. and S. Gopal, 2000. Fuzzy set theory and
thematic maps: accuracy assessment and area estimation.
International Journal of Geographical Information Science,
14(2), pp. 153-172.
ACKNOWLEDGEMENTS
This Research is funded by the 973 Program (Grant No.
2009CB723905), Sino-Germany Joint Project (Grant No.
2006DFB91920), National Key Project of Scientific and
Technical Supporting Programs (2007BAC23B05) and
NSFC project (Grant No. 40721001). The authors would like
to express their many thanks to CRESDA for providing HJ
image and Mr. Lian Feng, Mr. Xiaobing, Cai and Mr.
Shoujing, Yi for their assistants in the ground survey.
Wu, Y. and W. Ji, 2002. Study on Jiangxi Poyang Lake
National Nature Reserve. China Forestry Publishing House
Beijing.
Zadeh, L. A., 1965. Fuzzy sets. Information and Control, 8,
pp. 338-353.
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